Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.2 Exercises: 40

Answer

$\frac{ln(|tan(2x)+sec(2x)|)-ln(|cos(2x)|)}{2}+C$

Work Step by Step

$\int (tan(2x)+sec(2x))dx$ $=\int tan(2x)dx+\int sec(2x)dx$ let $2x=u$ $2dx=du$ $=\int tan(2x)dx+\int sec(2x)dx$ $=\frac{1}{2} \int tan(u)du + \frac{1}{2} \int sec(u)du$ $=(\frac{-ln(|cos(u)|)}{2})+(\frac{ln(|tan(u)+sec(u)|)}{2})+C$ $=\frac{ln(|tan(2x)+sec(2x)|)-ln(|cos(2x)|)}{2}+C$
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